MULTIPLICITY OF STEADY STATES IN CONTINUOUS CULTURE OF MAMMALIAN CELLS
Andrew Yongky, Tung Le, Simon Grimm, Wei-Shou HuDepartment of Chemical Engineering and Materials Science,
University of Minnesota
Major incentives for continuous operations
• Reduced turn around time• Steady state operation (a continuous operation need not to be at a steady state)
Continuous Process with recycle
F, s0(1+α) F, s, x
V, s, xF, s, x2
αF, s, cx
F, s0
F, s, x, xd
V, s, x
F, s0
F, s, x, xd
V, s, x
What is a steady state
• Has meaningful solution(s) when the system’s equations are set to 0
• Sometimes a system has a unique steady state for a set of operating conditions
• Other times, has mutliple steady state
Stead State Concentrations in Continuous Culture with Cell Recycle
0.0 1.0 2.0 3.0 4.0 5.0 6.00.0
0.5
1.0
1.5
2.0
2.5
3.0
Dilution RateCell
and
Subs
trat
e Co
ncen
trati
ons
With Cell Recycle
Simple Continuous CultureWashout
SubstrateSubstrate
Washout
Cell
Cell
0100
200300
400500
600700
800900
10000
20
40
60
80
100
120
140
0
0.01
0.02
0.03
0.04
0.05
0.06
Time (hr)
Flux
(mM
/h)
Grow
th R
ate
(hr-
1)
0 100 200 300 400 500 600 700 800 90010000
2
4
6
8
10
0
2
4
6
8
10
Time (hr)
Conc
entr
ation
(mM
)
Cell
Conc
(x10
6 ce
lls/m
L)
Lac
Glc
Cell conc
JLac
Growth Rate
JGlc
What is a steady state from an operational perspective
D = 0.033; Glc = 7 mM
Under one set of conditions (dilution rate, feed concentration), the state reaches constant valuesKey physiological parameters: growth rate, metabolism are constant
0100
200300
400500
600700
800900
10000
20
40
60
80
100
120
140
Time (hr)
Flux
(mM
/h)
0 100 200 300 400 500 600 700 800 90010000
2
4
6
8
10
0
2
4
6
8
10
Time (hr)
Conc
entr
ation
(mM
)
Cell
Conc
(x10
6 ce
lls/m
L)
Lac
Glc
Cell conc
JLac
Growth Rate
JGlc
What is a steady state from an operational perspective
D = 0.033; Glc = 7 mM
The same data if obtained from perfusion culture, may not be SSgrowth rate, metabolism may not be constant
Continuous Process with recycle
F, s0(1+α) F, s, x
V, s, xF, s, x2
αF, s, cx
The Theme
• Multiple metabolic state when cells grow at one set of growth rate, glucose and lactate concentrations
• The metabolic steady state multiplicity leads to cell concentration multiplicity
• If we ensure the same steady state is achieved in different runs, process will be more robust
Glucose
Pyruvate
Glutamine
TCA cycle
Lactate
Cell Mass
Amino Acids
AcetylCoA
NH3
CO2
O2
High flux state
Glucose
Pyruvate
Glutamine
TCA cycle
Lactate
Cell Mass
Amino Acids
AcetylCoA
NH3
CO2
O2
Low flux state
Glucose
Pyruvate
Glutamine
TCA cycle
Lactate
Cell Mass
Amino Acids
AcetylCoA
NH3
CO2
O2
Low flux state
0
2
4
6
Cel
l Con
c. (1
09 /L)
Fed-batch
Batch
0
1
2
3
0 100 200 300Time (hr)
DL/
DG
(mol
/mol
)
0
1
2
3
4
Glu
cose
(g/L
)
0
1
2
0 100 200 300Time (hr)
Lact
ate
(g/L
)
Continuous Culture with Metabolic Shift
Distinct Steady States Corresponding to Different Metabolic States
0
2
4
6
0 100 200 300Time (hrs)
Cel
l Con
c (1
06 /mL)
DL/DG0.030.050.150.300.50
1.50
The system: A ballA contour of surface on which it can move
Steady State, where “things” can be “steady”, “at equilibrium”
Stable steady state
Unstable steady state
No steady state
The system: A ballA contour of surface that it can move
Force: gravitational force, external force, friction force
The system: A ballA contour of surface that it can move
Force: gravitational force, external force, friction force
The stability of the system can be shown mathematically using equations describing the system
Stable steady state
Unstable steady state
When the “state” of a system changes, it moves along where the system has stable steady state.
Stability analysis can be applied to chemical reaction systems
The kinetic equations for all glycolysis, PPP and TCA cycle enzymes are all very well characterized
Allosteric Regulations in Glycolysis PathwayGlucose
Fructose-6-Phosphate
Pyruvate
Fructose-1,6-Bisphosphate
Fructose-2,6-Bisphosphate
Glucose-6-Phosphate
Phosphoenol PyruvatePyruvate Kinase
PFK2
Hexokinase
…
Lactate
InhibitionActivation
Phosphofructokinase
Pyruvatemito
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
30
50
70
Extracellular Glucose (mM)
Glyc
olys
is Fl
ux (m
M/h
)
Stable, low flux state
Unstable steady state, unrealizable
Stable, high flux state
When the “state” of a system changes, it moves along where the system has stable steady state.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
30
50
70
Extracellular Glucose (mM)
Glyc
olys
is Fl
ux (m
M/h
)
Allosteric Regulations in Glycolysis PathwayGlucose
Fructose-6-Phosphate
Pyruvate
Fructose-1,6-Bisphosphate
Fructose-2,6-Bisphosphate
Glucose-6-Phosphate
Phosphoenol PyruvatePyruvate Kinase
PFK2
Hexokinase
…
Lactate
InhibitionActivation
Phosphofructokinase
Pyruvatemito
Akt Down-regulated and p53 Up-regulated in Late Stage
Glucose
Fructose-6-Phosphate
Pyruvate
Fructose-1,6-Bisphosphate
Fructose-2,6-Bisphosphate
PFK1
Glucose-6-Phosphate
Phosphoenol Pyruvate
Pyruvate Kinase
PFK2p53
PGAM
Glucose
GLUT1
AktAMP
K
InhibitionActivation
HK
Myc Hif1a
PFK2
0 1 2 3 4 510
30
50
70
Extracellular Glucose (mM)
Glyc
olys
is Fl
ux (m
M/h
)Bistabilty in Central Metabolism
Unstable Steady States
High Flux State
Effect of Lactate on Glycolytic Flux
02
46
810
0
10
20
30
40
500
20
40
60
80
Lactate (mM) Glucose (mM)
Glyc
olys
is Fl
ux (m
M/h
)
Effect of Lactate on Glycolytic Flux
Lactate (mM) Glucose (mM)
Glyc
olys
is Fl
ux (m
M/h
)
Lactate (mM) Glucose (mM)
Glyc
olys
is Fl
ux (m
M/h
)
Effect of Lactate on Glycolytic Flux
Effect of AKT on Glycolytic Activity
Trajectory of Cells in Shifting to Low Flux State
Trajectory of Cells in Shifting to Low Flux State
Trajectory of Cells in Shifting to Low Flux State
Figure 6: Transient behavior demonstrating effect of glucose concentration perturbations on cellular metabolic state
50 40 20 10 0
Lac (mM)0
10
15 0
20
40
60
80
30
Glc (mM)
Glyc
olys
is Fl
ux (m
M/h
)
5
B
AC
D
E
F, s0
F, s, x, xd
V, s, x
Multi-scale Model: Metabolism Model in Continuous Culture
0 0.01 0.02 0.03 0.04 0.050
5
10
15
20
Dilution Rate (hr-1)
Cell
Conc
(x10
6 ce
lls/m
L)
0 0.01 0.02 0.03 0.04 0.050
20
40
60
80
Dilution Rate (hr-1)
JGlc
(mM
/hr)
Bistability in Continuous Culture
0 0.01 0.02 0.03 0.04 0.050
1
2
3
4
5
Dilution Rate (hr-1)
Gluc
ose
(mM
)
Multiscale model simulationGlc = 8 mM
0 0.5 1 1.5 2 2.50
20
40
60
80
Glucose (mM)
JGlc
(mM
/hr)
0 0.5 1 1.5 2 2.50
2
4
6
8
10
12
Glucose (mM)Ce
ll Co
nc (x
106
cells
/mL)
Bistability in Continuous Culture
0 0.01 0.02 0.03 0.04 0.050
5
10
15
20
Dilution Rate (hr-1)
Cell
Conc
(x
106
cells
/mL)
0 0.01 0.02 0.03 0.04 0.050
5
10
15
20
Dilution Rate (hr-1)
Cell
Conc
(x
106
cells
/mL)
0 0.01 0.02 0.03 0.04 0.050
20
40
60
80
Dilution Rate (hr-1)JG
lc (m
M/h
r)
0 0.01 0.02 0.03 0.04 0.050
20
40
60
80
Dilution Rate (hr-1)
JGlc
(mM
/hr)
0 0.01 0.02 0.03 0.04 0.050
5
10
15
20
Dilution Rate (hr-1)
Cell
Conc
(x
106
cells
/mL)
0 0.01 0.02 0.03 0.04 0.050
20
40
60
80
Dilution Rate (hr-1)
JGlc
(mM
/hr)
Effect of Glucose FeedGlc = 15 mM
Glc = 8 mM
Glc = 5 mM
Distinct Steady States Corresponding to Different Metabolic States
0
2
4
6
0 100 200 300Time (hrs)
Cel
l Con
c (1
06 /mL)
DL/DG0.030.050.150.300.50
1.50
0 200 400 600 800 10000
20
40
60
80
100
120
140
0
0.01
0.02
0.03
0.04
0.05
0.06
Time (hr)
Flux
(mM
/h)
Grow
th R
ate
(hr-
1)
0 200 400 600 800 10000
2
4
6
8
10
0
2
4
6
8
10
Time (hr)
Conc
entr
ation
(mM
)
Cell
Conc
(x10
6 ce
lls/m
L)
D = 0.033; Glc = 7 mM
Lac
GlcCell conc
JLac
Growth Rate
JGlc
Transient Trajectory of Culture with High Metabolic Flux
0100
200300
400500
600700
800900
10000
20
40
60
80
100
120
140
0
0.01
0.02
0.03
0.04
0.05
0.06
Time (hr)
Flux
(mM
/h)
Grow
th R
ate
(hr-
1)
0 100 200 300 400 500 600 700 800 90010000
2
4
6
8
10
0
2
4
6
8
10
Time (hr)
Conc
entr
ation
(mM
)
Cell
Conc
(x10
6 ce
lls/m
L)
Lac
Glc
Cell conc
JLac
Growth Rate
JGlc
Transient Trajectory of Culture with Low Metabolic Flux
D = 0.033; Glc = 7 mM
Benefit of slow growth rate?
Transcriptome analysis – effect of culture age?
Conclusion• Physiological steady state
- truly benefit continuous operation• Metabolic regulation and growth
causes metabolic steady state multiplicity
• Continuous cell culture reactor – multiple steady state
• Different trajectories lead to different steady state
Thank you!
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